| The goal of this dissertation is to provide new effective algorithms for extracting thin structures, such as lines and sheets, from three-dimensional biomedical images. Of particular interest is the capability to recover cellular structures, such as microtubule spindle fibers and plasma membranes, from laser scanning confocal microscopy data. These piecewise linear and planar structures with a Gaussian-like intensity profile can be differentiated from others by their distinctive shape characteristics. Shape-based methods are developed to enhance and segment line and sheet structures. Mathematical functions are formulated to derive quantitative relationships between shape characteristics and the eigenvalues of the Hessian matrix. Novel noise-resistant differentiation estimation methods, based on a function fitting strategy, are developed to improve the accuracy in extracting eigenvalue-related geometric features from the Hessian matrix. The segmentation algorithm is implemented in an enhancement/thresholding type of edge operators. Line and sheet structures are enhanced by their shape features and segmented by thresholding. The methods are tested on synthetic, angiography, MRI, and confocal microscopy data. A significant improvement in thin structure segmentation and visualization is demonstrated by the resultant images. They show that the new methods are robust and suitable for different types of data and a broad range of noise levels. |
